中文摘要：

考虑Quasi-Geostrophic方程,以经典解沿流线小时间的表现,给出Quasi-Geostrophic方程经典解沿流线爆破的一个充分条件.方法是从Quasi-Geostrophic方程推出一个解的梯度长度的倒数沿流线的微分不等式,从而推出结论.手法与结果都类似于Chae关于3维不可压Euler方程组经典解的爆破工作.该结果对进一步研究Quasi-Geostrophic方程相关问题,有一定的启示作用.

英文摘要：

The quasi-geostrophic equation is considered in this paper. A criterion is given for the finite time blow-up of a classical solution in terms of its small time behaviors along the trajectories. The result is deduced from a differential inequality for the reciprocal of the length of the gradient of the solution along a particle trajectories. The method and the result are similar to those of Chae on the 3 dimensional incompressible Euler system. The result gives some inspiration for the further research of quasi-geostrophic equation.